Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Then, we argue that the proportionality rule is one of the factors responsible for cascaded defaults, and that the overall system loss can be reduced if this rule is lifted. The proposed approach thus shifts the focus from the individual interest to the overall system's interest to control and contain adverse effects of cascaded failures, and we show that clearing payments in this setting can be computed by solving suitable convex optimization problems.

翻译：金融网络具有复杂的相互债务结构。这些债务通过称为清算的机制全部或部分（发生违约时）得到清偿，该机制通过遵守有限责任、绝对优先权和按比例分配（按比例付款）等规则确定一组支付来结算债权。然而，在金融系统受到冲击的情况下，清算机制可能导致违约连锁反应，并最终引发金融灾难。本文首先研究了Eisenberg和Noe提出的按比例付款清算模型，推导出清算支付唯一性的新颖充要条件，该条件适用于任意拓扑结构的金融网络。随后，我们论证按比例分配规则是导致违约连锁反应的因素之一，若取消该规则可减少整体系统损失。因此，所提出的方法将关注点从个体利益转向整体系统利益，以控制和遏制连锁故障的不利影响，并证明在此设定下，清算支付可通过求解适当的凸优化问题来计算。